Question

Circle A has a center at `(8 ,1 )` and an area of `100 pi`. Circle B has a center at `(4 ,2 )` and an area of `36 pi`. Do the circles overlap? If not, what is the shortest distance between them?

Answer 1

The circles overlap

Explanation:

Circle A
Area given as `100pi`
`rarr "radius " r_A = 10` (since Area `=pir^2`)

Distance between centers of circles
`d=sqrt((Delta x)^2+(Delta y)^2)`

`color(white)("X")=sqrt((8-4)^2+(1-2)^2)`

`color(white)("X")=sqrt(17)`

Since `sqrt(17) < 10`
The center of Circle B is inside Circle A.
so the circles must overlap.